to address your Q? specifcially, they can be attached, but do not have to be.
Egg tumblers come in all shapes and sizes and can be as simple as a bubbling airstone to as complex as you want them to be, and yes some also tap off a main line and spill back into a main resevior. The idea is to keep the eggs suspended in the water column, and w/ all that water movement comes good oxygen and waste/nutrient diffusion